Convergence Theory for the Structured BFGS Secant Method With an Application to Nonlinear Least Squares.

摘要

In 1981, Dennis and Walker developed a convergence theory for structural secant methods which included the PSB and the DFP secant methods, but not the straightforward structured secant method. Here we fill this gap in the theory by establishing a convergence theory for the structured BFGS secant method. A direct application of our new theory gives the first proof of local and q-superlinera convergence of the important structured BFGS secant method for the nonlinear least-squares problem which is used by Dennis, Gay and Welsh in the current version.